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CONFORMAL VERSUS TOPOLOGICAL CONJUGACY OF AUTOMORPHISMS ON COMPACT RIEMANN SURFACES

Published online by Cambridge University Press:  01 May 1997

GABINO GONZÁLEZ-DIEZ  and
RUBÉN A. HIDALGO
GABINO GONZÁLEZ-DIEZ
Affiliation:
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
RUBÉN A. HIDALGO
Affiliation:
Departamento de Matemáticas, Universidad Técnica Federico, Santa María Casilla 110-V, Valparaiso, Chile
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Abstract

We produce a family of algebraic curves (closed Riemann surfaces) Sλ admitting two cyclic groups H1 and H2 of conformal automorphisms, which are topologically (but not conformally) conjugate and such that S/Hi is the Riemann sphere [Copf ]ˆ. The relevance of this example is that it shows that the subvarieties of moduli space consisting of points parametrizing curves which occur as cyclic coverings (of a fixed topological type) of [Copf ]ˆ need not be normal.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 3 , May 1997 , pp. 280 - 284
Copyright
© The London Mathematical Society 1997

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